Unsteady Flow in Pipes - PowerPoint PPT Presentation

Loading...

PPT – Unsteady Flow in Pipes PowerPoint presentation | free to download - id: 3cd0fe-ZjAxN



Loading


The Adobe Flash plugin is needed to view this content

Get the plugin now

View by Category
About This Presentation
Title:

Unsteady Flow in Pipes

Description:

The Islamic University of Gaza Faculty of Engineering Civil Engineering Department Hydraulics - ECIV 3322 Chapter 4 Unsteady Flow in Pipes Some typical damages Some ... – PowerPoint PPT presentation

Number of Views:519
Avg rating:3.0/5.0
Slides: 34
Provided by: siteIuga81
Category:
Tags: flow | pipes | unsteady

less

Write a Comment
User Comments (0)
Transcript and Presenter's Notes

Title: Unsteady Flow in Pipes


1
The Islamic University of Gaza Faculty of
Engineering Civil Engineering Department
Hydraulics - ECIV 3322

Chapter 4
Unsteady Flow in Pipes
2
Water Hammer Phenomenon in pipelines
  • A sudden change of flow rate in a large pipeline
    (due to valve closure, pump turnoff, etc.) may
    involve a great mass of water moving inside the
    pipe.
  • The force resulting from changing the speed of
    the water mass may cause a pressure rise in the
    pipe with a magnitude several times greater than
    the normal static pressure in the pipe.
  • The excessive pressure may fracture the pipe
    walls or cause other damage to the pipeline
    system.
  • This phenomenon is commonly known as the water
    hammer phenomenon

3
Some typical damages
Burst pipe in power sation Big Creek 3, USA
Pump damage in Azambuja Portugal
Pipe damage in power station Okigawa
4
(No Transcript)
5
Water Hammer
  • Consider a long pipe AB
  • Connected at one end to a reservoir containing
    water at a height H from the center of the pipe.
  • At the other end of the pipe, a valve to regulate
    the flow of water is provided.

6
  • If the valve is suddenly closed, the flowing
    water will be obstructed and momentum will be
    destroyed and consequently a wave of high
    pressure will be created which travels back and
    forth starting at the valve, traveling to the
    reservoir, and returning back to the valve and so
    on.
  • This wave of high pressure
  • Has a very high speed (called celerity, C )
    which may reach the speed of sound wave and may
    create noise called knocking,
  • Has the effect of hammering action on the walls
    of the pipe and hence is commonly known as the
    water hammer phenomenon.

7
  • The kinetic energy of the water moving through
    the pipe is converted into potential energy
    stored in the water and the walls of the pipe
    through the elastic deformation of both.
  • The water is compressed and the pipe material is
    stretched.
  • The following figure illustrates the formation
    and transition of the pressure wave due to the
    sudden closure of the valve

8
Propagation of water hammer pressure wave
Steady state condition
Transient condition t lt L/C
9
Transient condition t L/C
Transient condition L/C gtt gt2L/C
Transient condition t 2L/C
10
Transient condition 2L/C gtt gt3L/C
Transient condition t 3L/C
11
Transient condition 3L/C gtt gt4L/C
Transient condition t 4L/C
12
Analysis of Water Hammer Phenomenon
  • The pressure rise due to water hammer depends
    upon
  • (a) The velocity of the flow of water in pipe,
  • (b) The length of pipe,
  • (c) Time taken to close the valve,
  • (d) Elastic properties of the material of the
    pipe.
  • The following cases of water hammer will be
    considered
  • Gradual closure of valve,
  • Sudden closure of valve and pipe is rigid, and
  • Sudden closure of valve and pipe is elastic.

13
  • The time required for the pressure wave to travel
    from the valve to the reservoir and back to the
    valve is
  • Where
  • L length of the pipe (m)
  • C speed of pressure wave, celerity (m/sec)
  • If the valve time of closure is tc , then
  • If the closure is considered gradual
  • If the closure is considered sudden

14
  • The speed of pressure wave C depends on
  • the pipe wall material.
  • the properties of the fluid.
  • the anchorage method of the pipe.
  • if the pipe is rigid
  • if the pipe is elastic
  • and

15
  • Where
  • C velocity (celerity) of pressure wave due to
    water hammer.
  • water density ( 1000 kg/m3 ).
  • Eb bulk modulus of water ( 2.1 x 109 N/m2 ).
  • Ec effective bulk modulus of water in elastic
    pipe.
  • Ep Modulus of elasticity of the pipe
    material.
  • e thickness of pipe wall.
  • D diameter of pipe.
  • K factor depends on the anchorage method
  • for pipes free to move longitudinally,
  • for pipes anchored at both ends against
    longitudinal movement
  • for pipes with expansion joints.
  • where poissons ratio of the pipe
    material (0.25 - 0.35). It may take the value
    0.25 for common pipe materials.

16
(No Transcript)
17
The Maximum pressure created by the water hammer
18
Case 1 Gradual Closure of Valve
  • If the time of closure , then the
    closure is said to be gradual and the increased
    pressure is
  • where,
  • V0 initial velocity of water flowing in the
    pipe before pipe closure
  • t time of closure.
  • L length of pipe.
  • water density.
  • The pressure head caused by the water hammer
    is

19
Another method for closure time (t gt 2 L/C)
20
Case 2 Sudden Closure of Valve and Pipe is Rigid
  • If the time of closure , then the
    closure is said to be Sudden.
  • The pressure head due caused by the water hammer
    is
  • But for rigid pipe so

21
Case 3 Sudden Closure of Valve and Pipe is
Elastic
  • If the time of closure , then the
    closure is said to be Sudden.
  • The pressure head caused by the water hammer is
  • But for elastic pipe so

22
Water hammer pressure head
  • Applying the water hammer formulas we can
    determine the energy gradient line and the
    hydraulic gradient line for the pipe system under
    steady flow condition.

Due to water hammer
HA
Water Hammer Pressure in a Pipeline
So the total pressure at any point M after
closure (water hammer) is
or
23
Time History of Pressure Wave (Water Hammer)
  • The time history of the pressure wave for a
    specific point on the pipe is a graph that simply
    shows the relation between the pressure increase
    ( ) and time during the propagation of the
    water hammer pressure waves.

24
  • For example, considering point A just to the
    left of the valve.
  • Note friction (viscosity) is neglected.

1
Time history for pressure at point A (after
valve closure)
25
The time history for point M (at midpoint of
the pipe)
1
Note friction (viscosity) is neglected.
26
The time history for point B (at a distance x
from the reservoir )
t(2L/C)
1
Note friction (viscosity) is neglected.
This is a general graph where we can substitute
any value for x (within the pipe length) to
obtain the time history for that point.
27
In real practice friction effects are considered
and hence a damping effect occurs and the
pressure wave dies out, i.e. energy is
dissipated.
Damping effect of friction
t(2L/C)
the time history for pressure at point A when
friction (viscosity) is included
28
Stresses in the pipe wall
  • After calculating the pressure increase due to
    the water hammer, we can find the stresses in the
    pipe wall
  • Circumferential (hoop) stress fc
  • Longitudinal stress fL

where D pipe inside diameter tp pipe
wall thickness
total pressure initial pressure (before
valve closure) pressure increase due water
hammer.
29
Example 1
30
Solution
31
To keep the water hammer pressure within
manageable limits, valves are commonly design
with closure times considerably greater than 2L/C
32
Example
  • A cast iron pipe with 20 cm diameter and 15 mm
    wall thickness is carrying water from a
    reservoir. At the end of the pipe a valve is
    installed to regulate the flow. The following
    data are available
  • e 0.15 mm (absolute roughness) ,
  • L 1500 m (length of pipe),
  • Q 40 l/sec (design flow) ,
  • K 2.1 x 109 N/m2 (bulk modulus of water),
  • E 2.1 x 1011 N/m2 (modulus of elasticity of
    cast iron),
  • 0.25 (poissons ratio),
  • 1000 kg/m3
  • T 150 C.

33
  • Find , , fc , and fL due
    to the water hammer produced for the following
    cases
  • Assuming rigid pipe when tc 10 seconds, and tc
    1.5 seconds.
  • Assuming elastic pipe when tc 10 seconds, and
    tc 1.5 seconds, if
  • the pipe is free to move longitudinally,
  • the pipe is anchored at both ends and throughout
    its length,
  • the pipe has expansion joints.
  • Draw the time history of the pressure wave for
    the case (b-3) at
  • a point just to the left of the valve, and
  • a distance x 0.35 L from the reservoir.
  • Find the total pressure for all the cases in
    (b-3).
About PowerShow.com